Electroweak Corrections to $B_{s,d} \to \ell^+ \ell^-$

We calculate the full two-loop electroweak matching corrections to the operator governing the decay B_q --> l^+ l^- in the Standard Model. Their inclusion removes an electroweak scheme and scale uncertainty of about 7% of the branching ratio. Using different renormalization schemes of the involved electroweak parameters, we estimate residual perturbative electroweak and QED uncertainties to be less than 1% at the level of the branching ratio.
Comment: 16 pages, 6 figures, supplementary Mathematica file "c10.m" with analytical results; v2: references updated